The Former French international joined the Swans in January on a short-term deal which was due to expire this summer but has now committed his immediate future at Liberty Stadium.
However, he has now put pen to paper on a new agreement which will see him stay on as a member of Clement's backroom team.
Makelele is one of Clement's assistants alongside Nigel Gibbs, goalkeeper coach Tony Roberts and head of physical performance Karl Halabi.
The 44-year-old enjoyed a spectacular playing career which included stints at Real Madrid, Chelsea and Paris Saint-Germain.
Clement was on the coaching staff at Stamford Bridge when Makelele was a player, while they were also colleagues in Carlo Ancelotti's backroom team at PSG.
Clement, the former Derby manager, believes Makelele was an influential figure in the Swans' successful Premier League survival push.
"We are very happy that he is going to be staying on because he is very popular," the Swans boss said last week.
"He is a quiet, humble man considering what he did as a player. He has great experience and he has passed that on to the players."
Makelele, who won 71 France caps, arrived in Wales after offering his services to Clement following his appointment at the beginning of January.
He won a string of trophies including two La Liga titles, two Premier Leagues and the Champions League.
Clement took charge of 19 league matches in his debut campaign in south Wales, securing nine victories, two draws and eight losses.
Fernando Llorente's late winner against West Brom on the final day of the campaign ensured that Swansea City finished 15th in the 2016-17 Premier League table.